Enhancing Secondary Students’ Understanding of Descriptive Statistics Using Contextual and Socio-critical Modeling: The Case of West Shewa Zone, Ethiopia Mulugeta Woldemicheal A Thesis Submitted to The Department of Science and Mathematics Education Presented in Fulfillment of the Requirements for the Degree of Doctor of Philosophy (Science and Mathematics Education) Addis Ababa University Addis Ababa, Ethiopia July, 2015 i Addis Ababa University School of Graduate Studies This is to certify that the dissertation research prepared by Mulugeta Woldemicheal Gebresenbet, entitled: Enhancing Secondary Students’ Understanding of Descriptive Statistics Using Contextual and Socio-critical Modeling: The Case of West Shewa Zone, Ethiopia, and submitted in fulfillments of the requirements for the degree of Doctor of Philosophy in Science and Mathematics Education compiles with the regulations of Addis Ababa University and meets the accepted standard with respect to originality and quality. Signed by the examining committee: External Examiner: Signature Date Internal Examiner: Signature Date External Advisor: Signature Date Local Advisor: Signature Date Chair of Department or Graduate program Coordinator i Declaration I declare that this dissertation is my original work and it has not been previously submitted to meet the requirement for an award at Addis Ababa University or at any other universities. To the best of my knowledge and belief, the dissertation contains no material previously published or written by another person except where due reference is made. Mulugeta Woldemicheal July, 2015 ii Abstract Enhancing Secondary Students’ Understanding of Descriptive Statistics Using Contextual and Socio-critical Modeling: The Case of West Shewa Zone, Ethiopia Mulugeta Woldemicheal Addis Ababa University, 2015 The issue that this study addresses is the need for secondary students to work on relevant non-routine statistical problems to enhance their understanding of descriptive statistics. The purpose of this study is to explain how secondary students can enhance their understanding of descriptive statistics using Modeling Approach and to compare the amount of learning achieved using Modeling and Non-modeling Instructional Approaches. The Modeling Approach integrated the Contextual and Socio-critical Modeling Perspectives to teach a unit of descriptive statistics in secondary mathematics curriculum. The leading research question set forth is, to what extent and how do high school students enhance their understanding of descriptive statistics using a Modeling Approach? This transformative embedded mixed method study looked into three facets of students’ understanding of descriptive statistics: procedural, conceptual and critical. The study was conducted at two high schools in urban district in West Shewa Zone, Ethiopia. For comparisons, four Grade Nine sections with a total of 163 students were selected by purposive sampling technique. An instrument called Teaching for Robust Understanding in Mathematics (TRU Math) was used for observing Model-eliciting Activities (MEAs) to capture the Modeling Approach classroom practice (Schoenfeld, 2013). Quality Assurance Guide instrument was used to assess students’ models on MEAs (Lesh et al., iii 2000). Standard questions were used for achievement tests on procedural and conceptual understanding of descriptive statistics. An attitude survey instrument was administered to see students’ change of attitude towards statistics using Modeling Approach. Teams of students did projects on their own themes for six weeks. The quantitative data of the study was analyzed using descriptive statistics, t-tests and ANOVA. The qualitative data of the study was analyzed using thematic and content analyses. A statistically significant difference was found on conceptual understanding achievement test with medium effect size using Modeling Approach, but no statistical significant difference was found on procedural understanding achievement test except female comparison. Significant statistical effects were observed for attitude scale and subscales. Students enhanced their critical understanding of descriptive statistics doing projects through data modeling. The findings of this study suggested students more likely enhanced their understanding of descriptive statistics using Modeling Approach. iv Acknowledgments First and foremost, I thank the Creator of the world Who helped me to see my dreams come true and for His true gift of life to accomplish this study. This dissertation would not have been possible or completed without a lot of assistance from my advisors, family, colleagues, friends, teachers and the study participants. Thank you my advisors, Dr. Jennifer Noll and Dr. Mulugeta Atnafu, for your unwavering support and advice. Especially, I would like to thank Dr. Jennifer Noll, who is an inspirational person to work on Statistics Education. She has assisted me a lot with much patience from the beginning to the final stage of the dissertation. Dr. Mulugeta Atnafu, I thank you for trusting and supporting me to move forward to finish this study successfully. My gratitude also goes to Dr. Kassa Micheal for you made yourself always available for providing me suggestions and insights. I would like to thank Professor Eshetu Wencheko, Professor Asmamaw and Mr. Steve Johnson for giving me constructive comments. Thank you my family for giving me the kind of energy to do this research by way of strengthening my commitment. Thank you my wife, Mitike Mekonnen, for sharing with me the happy and sad moments of the study. Thank you my mother, I never forget your mentorship in my childhood to love mathematics and have a dream to study mathematics. Thank you my father, you taught me how to discipline myself to finish this dissertation as you always have been a dedicated teacher. Last, but not least, I thank teachers and the study participants who allowed me to collect data for this dissertation research. v Table of Contents Abstract .............................................................................................................................. iii Acknowledgments............................................................................................................... v Table of Contents ............................................................................................................... vi List of Figures .................................................................................................................... ix List of Tables ...................................................................................................................... x List of Acronyms and Abbreviations ................................................................................ xii CHAPTER 1: INTRODUCTION ....................................................................................... 1 1.1 Introduction ............................................................................................................... 1 1.2 Background of the Study ........................................................................................... 1 1.3 Context of the Study .................................................................................................. 4 1.4 Statement of the Problem .......................................................................................... 7 1.5 Aims and Purpose of the Research .......................................................................... 10 1.5.1 Research Questions........................................................................................... 11 1.5.2 Research Hypotheses ........................................................................................ 11 1.6 Significance of the Study ........................................................................................ 15 1.7 Delimitations of the Study....................................................................................... 15 1.8 Limitations of the Study .......................................................................................... 16 1.9 Definitions of Terms ............................................................................................... 17 1.10 Structure of the Dissertation .................................................................................. 17 CHAPTER 2: LITERATURE REVIEW .......................................................................... 19 2.1 Introduction ............................................................................................................. 19 2.2 Statistical Literacy, Reasoning and Thinking ......................................................... 20 2.3 Statistics Learning Outcomes and Mathematics Proficiency Strands ..................... 23 2.4 Understanding Basic Concepts of Descriptive Statistics ........................................ 27 2.5 Research on Students’ Understanding of Descriptive Statistics ............................. 32 2.6 Theoretical Framework and Modeling Research .................................................... 43 2.6.1 Theoretical Framework..................................................................................... 43 2.6.2 Modeling Research ........................................................................................... 52 2.7 Conceptual Framework and Conclusion ................................................................. 57 vi CHAPTER 3:RESEARCH DESIGN AND METHODS .................................................. 61 3.1 Introduction